## ＜電子ブック＞Stable Convergence and Stable Limit Theorems

責任表示 by Erich Häusler, Harald Luschgy Häusler, Erich Luschgy, Harald SpringerLink (Online service) English (英語) Springer International Publishing Imprint: Springer 2015- Cham, Germany シリーズ Probability Theory and Stochastic Modelling ; 74 The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistic...s to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level with a solid knowledge of measure theoretic probability.続きを見る Preface1.Weak Convergence of Markov Kernels2.Stable Convergence3.Applications4.Stability of Limit Theorems5.Stable Martingale Central Limit Theorems6.Stable Functional Martingale Central Limit Theorems7.A Stable Limit Theorem with Exponential Rate8.Autoregression of Order One9.Branching ProcessesA. AppendixB. AppendixBibliography.続きを見る http://hdl.handle.net/2324/1001569915 Full text available from Springer Mathematics and Statistics eBooks 2015 English/International

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レコードID 3641550 QA273.A1-274.9 QA274-274.9 519.2 Distribution (Probability theory. Mathematical statistics. Probability Theory and Stochastic Processes. Statistical Theory and Methods. ssj0001525115 9783319183305[3319183303](print) 9783319183282[3319183281](print) 9783319365190[3319365193](print) 9783319183299[331918329X] 2020.06.27 2020.06.28